Variable duty cycle antilock braking system with accelerometer and fail-safe

ABSTRACT

Improvements in vehicle antilock braking systems of the type having an operator controlled master cylinder (11) and a second source (55, 57) of pressurized hydraulic fluid for selectively supplying rebuild pressure after an antilock event are disclosed. The improved system is selectively operable in one of three braking modes, a normal braking mode (119) where braking force is proportional to an operator brake pedal pressure, an enhanced anti-skid braking mode (69) where braking force may be maintained at a maximum nonskid level, and a conventional anti-skid braking mode (71) where braking force follows a cyclic pattern of fluid pressure bleed and build. The system includes circuitry (17, 19, 35, 37, 93, 95) for determining the speed of each wheel and an arrangement (59) operable independently of any vehicle wheels for determining vehicle deceleration. This comparison normally invokes the enhanced anti-skid braking mode. In the enhanced mode, the system is continually searching for an optimum wheel speed reference (39) by determining (119) on which side of the peak of a mu-slip curve the vehicle is operating, for example, by calculating the sign of the slope of the mu-slip curve at the current vehicle operating point, and then incrementing (88) a prior wheel speed reference by a value (79) which changes the wheel speed reference toward the peak (75) of the mu-slip curve thereby calculating an updated wheel speed reference to control appropriately the braking system. The accuracy of the determined vehicle deceleration, and in particular, of the accelerometer is confirmed by comparison (63) to an expected deceleration based on operator brake pressure, and the conventional anti-skid braking mode is substituted for the enhanced anti-skid braking mode in the event the determined vehicle deceleration is determined to be inaccurate. The enhanced anti-skid mode utilizes a pulse width modulated solenoid actuated two position valve (41, 43) operable in one position to provide a fluid flow path from the braking device, and in the other position to provide a fluid flow path from a second source to the braking device.

This application is a division of application Ser. No. 08/353,861 filedDec. 12, 1994, now U.S. Pat. No. 5,487,598.

BACKGROUND OF THE INVENTION

The present invention relates generally to vehicular braking systems andmore particularly to vehicle braking systems having anti-skid orantilock features.

Many known anti-skid devices simulate a driver induced anti-skidtechnique by cyclically increasing and decreasing the braking forceexerted on the wheels so that a slipping wheel having a tendency to lockis permitted to re-accelerate back to a speed corresponding to the speedof the vehicle. This is typically achieved by control valves alternatelyallowing fluid to flow out of and then into the brake cylinder, causinga lowering and raising the pressure of the fluid supplied to operate thebrake cylinder associated with the wheels of a vehicle. In such aconventional antilock braking system, the controlled wheel occasionallybegins slipping too much and operates for short times with acomparatively large amount of slip, this means a level of slip highenough to effect or reduce lateral forces available for steering andvehicle stability. In addition, excessive slip is frequently associatedwith reduced braking effectiveness, increased tire wear and shockloading on suspension components, difficulty in steering control, and isgenerally disturbing to the vehicle occupants.

While such cycling causes momentary reduction in braking effectivenessas well as reduced stability and steerability, and other undesirableeffects, it is useful in allowing re-setting of the calculated vehiclevelocity. Many antilock braking systems are invoked when a calculatedwheel speed differs sufficiently from a sensed wheel speed. In thetypical system, wheel speeds are used to determine slip by comparison toa computed vehicle velocity either directly or indirectly. Without aconstant re-checking of the computed vehicle velocity, errors willaccumulate and cause serious degradation leading to substantiallyreduced braking and/or reduced lateral force.

It is desirable to provide a system that is immune to the problem ofaccumulated errors and which acts as a continuous process with thecorrective action taken being proportional to the deviation from adesired performance. Such a process is relatively easy to control usingconventional feedback methods such as Proportional-Integral-Differential(PID) controllers. With such a system, a differential correction isreadily included allowing the system to anticipate future conditions byreacting to the rate of change of the error condition. Also, an integralterm can reduce the steady state error.

Some antilock braking systems also operate on a so-called pump-backprinciple where the same hydraulic fluid is returned to the brake padactuators subsequent to an anti-skid event while others operate on areplenish principle where the reapply or build fluid comes from aseparate source, frequently a hydraulic accumulator. The latter requiresonly a moderate sized pump while the pump-back type systems require amore expensive pump capable of supplying the maximum instantaneous flowrate.

It is desirable to provide a simple, quiet replenish type systemutilizing a low cost accelerometer which system maintains maximumbraking force near the peak of the mu-slip curve at all times.

SUMMARY OF THE INVENTION

In general, the present invention discloses a method of calculatingwheel speed reference for the control of a vehicle antilock brakingsystem includes measuring the current vehicle deceleration. A vehiclewheel speed reference is repeatedly computed by comparing the sign ofthe most recent change in computed force to the most recent change incomputed vehicle wheel speed reference, and updating the previouslycomputed wheel speed reference by incrementing that previous value. Acomparison of the most recent change in vehicle acceleration to the mostrecent change in wheel slip may also be employed to determine theappropriate incrementation. The vehicle braking system is thenappropriately controlled by repeatedly measuring each wheel speed,repeatedly comparing the calculated wheel speed reference to themeasured wheel speed, and controlling the antilock (anti-skid) brakingmode operation accordingly. An operator commanded vehicle decelerationis determined and the braking system is converted from an existingbraking mode to an anti-skid braking mode in the event the measuredvehicle deceleration differs from the operator commanded vehicledeceleration by more than a specified amount.

Also in general and in one form of the invention, an improved vehicleantilock braking system has a control arrangement for identifying awheel skid condition and a first flow control valve which changesposition in response to an identified wheel skid condition. While theskid condition prevails, the second flow control device is duty cyclemodulated between the two positions with a duty factor selected tomaintain the fluid pressure to the braking device at a maximum nonskidlevel. The control means for identifying the wheel skid conditionincludes one arrangement for measuring the speed of the wheel andanother arrangement for measuring the vehicle deceleration rateindependent of wheel speed. The measured deceleration rate is utilizedto compute a wheel speed reference. The wheel speed reference and themeasured speed of the wheel are then used in a feedback loop for brakingcontrol.

BRIEF DESCRIPTION OF THE DRAWING

FIG. 1 is a schematic representation of an overall brake and anti-skidsystem illustrating the present invention in one form;

FIG. 2 is a graph of brake actuator pressure as a function of thesolenoid enabling duty cycle;

FIG. 3 is a graph of control valve rebuild fluid flow rate as a functionof the solenoid enabling duty cycle;

FIG. 4 is a flow chart illustrating the alternative modes of operationof the system of FIG. 1;

FIG. 5 is a schematic representation of a control portion of a brake andanti-skid control system illustrating a modification of the system ofFIG. 1;

FIG. 6 is a flow chart illustrating a wheel speed reference optimizingalgorithm for the system of FIG. 5;

FIG. 7 is a mu-slip curve depicting tire friction as a function of tireslip; and

FIG. 8 is a schematic illustration of a control loop for one wheel.

Corresponding reference characters indicate corresponding partsthroughout the several views of the drawing.

DESCRIPTION OF THE PREFERRED EMBODIMENT

A portion of an antilock braking system for a passenger car or similarvehicle is shown schematically in FIG. 1. The system has solenoidactuated anti-skid or isolation valves 10 and 16 between anoperator-controlled pressure source or master cylinder 11 andcorresponding front wheel 13 and rear wheel 15 hydraulic brakeactuators. Typically, the pressure source 11 is a conventional mastercylinder having two separate circuits, one for the left front vehiclewheel brake 13 and the right rear vehicle wheel brake 15, and the other,which is substantially identical and not shown for the right front/leftrear vehicle wheel brakes. There are conventional proportioning valvessuch as 21 which are present to reduce the likelihood of a rear wheelskid by applying a only a portion of the line pressure to the rear wheelbrake cylinders when the hydraulic pressure is above some predeterminedthreshold. The vehicle wheels also have rotational speed sensors such as17 and 19 for providing control unit 33 with electrical indications ofthe angular velocities of individual wheels.

When the driver wishes to slow the vehicle, the linkage 23 from pedal 23supplies pistons in master cylinder 11 with an input force to pressurizefluid therein which communicated from the master cylinder 11 by way ofconduits (brake lines) 25 and 27 to a pair of pressure sensors 29 and31, and thence to the respective pairs of brake actuators (wheelcylinders) by way of four individual solenoid actuated valves such as 10and 16. The individual wheel isolation valves such as 10 and 16 arenormally in the position shown and transmit the fluid pressure directlyto the wheel cylinders to brake the vehicle. In the event, theelectrical indications from the speed sensors (17, 19,) supplied to theelectronic control unit 33 detects a sufficient difference between wheeldeceleration and measured vehicle deceleration to indicate a skid, anactuating signal is sent to the appropriate ones of four solenoidactuated anti-skid valves such as 10 and 16 to shut off the hydraulicfluid path from the master cylinder 11 to the wheel cylinder, and toestablish instead a bleed path from the wheel cylinder by way ofconduits such as 45, 47 and 49 to a common low pressure reservoir suchas the sump 51 thereby relieving the brake actuator pressure allowingthe slipping wheel to accelerate. At a time when wheel speed getssufficiently close to the vehicle speed and remains there for apredetermined time, the solenoid is de-energized and anti-skid valve 10or 16 resumes its normal braking condition where the conduit 45, forexample, is reconnected to master cylinder 11 through conduit 27.Periodically, during the time fluid is being bled from the brakeactuator, a valve such as 41 or 43 is actuated to connect conduits 47and 53 so that rebuild pressure is supplied from accumulator 55 throughthe series connected valves 41 and 10 or 43 and 16 to the individualwheel cylinders. The pressure in accumulator 55 is maintained by pump 57and its associated driving motor.

The solenoids such as 123,123' of valves 41 and 43 are periodicallyenergized and deenergized until controller circuit 33 indicates the sliphas been adequately reduced. So long as the corresponding isolationvalve 10 or 16 is enabled as by current flow in an illustrative controlsolenoid 121, the solenoid valve 41 or 43 is operated at a constantfrequency and the relative on-time is changed so that the averagepressure at the brake port varies in concert with the duty factor orpercentage of on-time. The selection of an appropriate duty factor toretain maximum braking force is determined by control unit 33 in amanner to be described subsequently. The maximum amplitude of pressureoscillations is determined by the frequency of valve operation and theorifices used in the valve. If the frequency is sufficiently high, brakecompliance is adequate to attenuate the oscillations so there is littleor no variation in braking due to the oscillations.

An accelerometer 59 measures vehicle acceleration and that measure ispassed through the low-pass filter 61 to filter out effects of enginevibrations, rough roads and other extraneous effects. Similar filters(not shown) may be used on the several wheel speed sensors such as 17and 19. Thereafter, the filtered acceleration signal is first multipliedby the mass of the vehicle at 73 to compute the decelerating force onthe vehicle, and that current force value is utilized to provide thecurrent wheel speed reference on line 39 by the recursive relationship:

    V.sub.r (k)=V.sub.r (k-1)+ΔV * sign(ΔF/ΔV.sub.r)(1)

where:

V_(r) (k-1)is the currently computed wheel speed reference;

V_(r) (k-1)is the wheel speed reference computed during the

immediately previous iteration;

ΔV_(r) is the change in wheel speed reference computed from thedifference between V_(r) (k-1); and

V_(r) (k-2), and ΔF is the change in decelerating force computed fromthe difference between F (k) and F (k-1).

The force F(k)is the force calculated from the vehicle accelerationmeasurement at time k, the current time. The force F(k-1) would be theresult of the acceleration computed at time k-1 (one sample periodearlier) and used until time k. Thus, the values used for the wheelspeed reference are those determined a sample period prior to thecorresponding stopping force values. ΔV is an incremental value which isadded to or subtracted from the previously computed wheel speedreference accordingly as the sign of the force/velocity gradient ispositive or negative to provide a new wheel speed reference value. Whiledivision to obtain the force/velocity gradient is indicated at 87, onlythe signs of the changes need be considered. If both are the same, thesign of the quotient is positive and it is negative if they differ. Thespecific value of ΔV may vary or may be fixed. The circuitry forimplementing equation (1)is shown generally at 91 and 92.

To better understand the reason for selecting the force/velocitygradient to indicate the direction of incrementation, consider FIG. 7.An increase in wheel speed corresponds to an decrease in the slip. Thus,if the force/velocity gradient is positive, the force/slip gradient isnegative and the vehicle is operating on the right side of the maximumbraking friction line 75. The computed wheel speed reference would beincremented, reducing the slip and moving the point of operation closerto the maximum friction line 75. To the left of this line, theforce/slip gradient (slope of the mu-slip curve)is positive. On thisside, a negative force/velocity gradient causes decrementation of thewheel speed reference (corresponding to an increase in slip) againmoving the operating point closer to the peak friction line.

As will be discussed in greater detail in conjunction with FIGS. 5 and6, the sign of the quotient of vehicle acceleration divided by wheelslip provides an alternative to the force/velocity gradient. Whenoperation is in the undesirable region to the right of the maximumbraking friction line 75, an increase in slip corresponds to a decreasein braking friction, a decrease in deceleration, and therefore, anincrease in acceleration. Under these conditions, the wheel speedreference will be appropriately incremented to reduce the slip.Similarly, operation to the left of line 75 will call for an increase inslip which is equivalent to a reduction in the wheel speed reference.

The step size or incremental value ΔV is typically different fordiffering signs of the force/velocity gradient. One effective way tocalculate step size is to make the maximum deceleration rate of thewheel speed reference proportional to the deceleration rate of thevehicle. If the deceleration rate of the wheel speed reference is twicethat of the vehicle, for example, then the reference will change in thedownward direction relative to the vehicle speed at a rate equal to thatof the vehicle. The same step size in the upward direction, however,would allow the reference to increase relative to vehicle speed at arate three times the deceleration rate of the vehicle. Such an upwardstep which is equal to the downward step is unnecessarily large and willcontribute to higher control errors. Preferably, the rate at which thereference can move relative to the vehicle velocity should be roughlybalanced in the up and down directions. Such a balance will tend tocancel errors caused by the wheel speed reference occasionally changingin the wrong direction. An upward step of about 10% of the downward stepwill provide an upward rate of 1.2 times the vehicle deceleration and adownward rate equal to vehicle deceleration.

The period for incrementing the wheel speed reference, if too large,will not allow the vehicle wheel speed reference to keep up with theactual vehicle speed resulting in reduced braking efficiency while asmaller period leads to more frequent and smaller amplitude oscillationsin the wheel speed and, as a result, higher braking efficiency. If theincrement period is too small, particularly in relation to the time lagof the wheel speed control loop, loss of control may result. The minimumperiod is also limited by the time required for the filter 61 to modifyor filter the output signal from accelerometer 59. With a wheel speedcontrol increment period of 0.010 seconds, wheel speed referenceincrement periods of about 0.100 seconds are preferred.

Of course, the recursive relationship assumes initialization; that is,some reference velocity and change in reference velocity must bedetermined independently of the relationship, or initial values assumedand the relationship allowed to settle into a steady state condition.For example, it is possible to establish vehicle velocity by measuringvehicle wheel speed, and then to utilize that established vehiclevelocity as the initial previously computed wheel speed reference in theupdating step.

The recursive relationship provides stepped wheel speed referenceestimates. The preferred step size is directly proportional to theincrement period. Any abrupt changes may be smoothed somewhat by anincreased iteration rate of the recursion relationship. The wheel speedreference estimates may also be smoothed between endpoints of the sampleperiod by replacing the step with a ramp which gradually increases ordecreases over the sample period. Thus, updating is performed graduallyby increasing the previous reference at a rate equal to the incrementdivided by the time between two consecutive computations of vehiclewheel speed reference in the event the sign of the gradient is positive,and by gradually decreasing that previous reference value at a rateequal to the decrement divided by the time between two consecutivecomputations of wheel speed reference in the event the sign of thegradient is negative.

FIG. 5 illustrates the modifications to FIG. 1 to accomplish the ramprather than step increment. The increment or decrement is integrated at77 over the sample period and that value is added to the previousestimate of the wheel speed reference at 79. FIG. 5 illustrates anothermodification to the system of FIG. 1. A so-called neutral step (V_(n))may be computed at 83 by the equation:

    V.sub.n =A*T*(0.85)                                        (2)

where: A is the vehicle acceleration;

T is the sample period of the closed loop wheel speed controller of FIG.8 (typically about 0.010 seconds); and a correction factor of 0.85(although other factors may be more appropriate for other situations) isan estimate of the fraction of vehicle speed corresponding to the peaksof the mu-slip curve.

The magnitude of this neutral step is selected so as to just keep pacewith the current vehicle deceleration. In the embodiment of FIG. 5, thewheel speed reference is determined by the following relationship:

    V.sub.r (k)=V.sub.r (k-1)+V.sub.n +βoptstep           (3)

where: optstep may be zero, an increment added to the neutral step ifthe acceleration/slip gradient is positive, or an increment subtractedfrom the (negative) neutral step if the acceleration/slip gradient isnegative and is computed as in FIG. 6. β is the ratio of the period ofthe wheel speed controller and the optimizing period. The optimizingstep is typically calculated about every 0.1 seconds, far lessfrequently than the neutral step. In FIG. 5, a fraction β of optstep isadded at 79 to the neutral step and used to increment the wheel speedreference at 88. Thus, when optstep =0, only the neutral step isselected, and is subtracted from the previous value of the wheel speedreference at 88, the new wheel speed reference is based on the currentvehicle deceleration. The algorithm is not "hunting" rather, it is justkeeping up with deceleration by decrementing the previously computedwheel speed reference.

There are three different names for the increment used: ΔV, neutral stepand optstep. The concept of Equation (1) uses ΔV to move the wheel speedreference in the direction to achieve optimal ABS performance and usesmuch smaller steps when raising the reference that when lowering it tocompensate for vehicle deceleration. The concept of Equation (3) uses aneutral step to compensate for vehicle deceleration and optimizing stepto move the reference in the optimizing direction allowing theoptimizing step upward and downward to be of equal size.

The wheel speed reference on line 39 provides the input to a closed loopwheel speed controller 33, the basic feedback arrangement of which isshown in FIG. 8. This closed loop wheel speed control applies to theembodiment of either FIG. 1 or FIG. 5. Of course, many of the featuresof either embodiment may be readily incorporated into the otherembodiment. The ABS valve signals on lines 123 are applied to thebraking hardware 125. Hydraulic line pressure is returned on line 127and applied to the adder 129 as a measure of brake torque. A measure ofvehicle acceleration is integrated at 133 to determine vehicle wheelspeed. For example, the sum of the road friction torque 131 and braketorque may be integrated at 133 and divided by the wheel inertia J toprovide a wheel speed indication. The difference between the wheel speedand wheel speed reference is determined at 139 to provide the errorsignal on line 135. One technique for determining road friction force131 is to repeatedly measure the hydraulic pressure being applied to awheel cylinder. The wheel velocity is similarly repeatedly measured.From the velocity measurements, wheel acceleration is determined andsuccessive values of acceleration are compared. Times at which theacceleration is zero are determined. For example, when the sign of theacceleration changes, there was a time between the two successivemeasurements at which it was zero. At that time, wheel cylinder isdirectly proportional to road friction.

FIG. 2 shows a graph of brake actuator pressure as a function of thesolenoid enabling duty cycle (percentage of each cycle during which thesolenoid of valve 41 or 43 is energized) under steady state conditionswhile FIG. 3 illustrates the relationship between the duty cycle and therate of hydraulic fluid flow in line 53. Control valves such as 41 and43 have a pair of flow restricting orifices, one controlling the rate ofdecay flow in line 49, and the other controlling the build rate throughline 53. These two graphs are for a valve having about equal size flowrestricting orifices and show that for such equal restrictions, themaximum flow rate occurs at about 50% duty cycle and for about 50% applypressure. With an orifice size selected to provide adequate responsewith moderate flow rates, it appears that the flow requirements aresomewhat high for pump-back systems, however, the flow requirements areaptly suited to a moderately sized pump 57 in conjunction with anaccumulator 55 to store pressurized fluid for momentary peaks in flow.

For many applications it is desirable to obtain better resolution atlower pressures, since delicate control is needed here to optimizestopping distance while maintaining controllability. Such betterresolution at lower pressures may be obtained by using a relativelysmaller restriction in the apply line 53 than in the decay line 49. Thisreduces maximum flow and shifts the maximum flow of FIG. 3 in thedirection of higher apply pressure, and can reduce the accumulator 55and pump 57 capacity requirements.

The several modes of operation of the braking system are illustrated inFIG. 4. From a non-braking condition, an operator depresses the brakepedal and rod 23 actuates the master cylinder 11 to supply brakingpressure on lines 25 and 27. Pressure sensors 29 and 31 supply pressureinformation to control 33 which is utilized in the accelerometer test 63and for duty factor limiting purposes at 65. Conventional braking 119continues as long as it is commanded unless a slip is detected at 67.Initial slip detection causes the system to enter the enhanced anti-skidbraking mode at 69. Since acceleration data is important for this modeof operation, accelerometer behavior is monitored at 63. The normalrelationship between acceleration and master cylinder pressure during anon-ABS situation is used to detect failure of accelerometer 59. Theindicated deceleration is compared to the sum of the decelerationcontributions of each wheel as calculated from the measured pressuresfrom sensors 29 and 31 by control unit 33. Should there be more than aprescribed difference between these values, the accelerometer fails test63. Upon detection of a failure of the accelerometer, the systemconverts to a conventional antilock braking mode of alternate build anddecay at 71. A viable, but less desirable option upon accelerometerfailure is to lock out all anti-skid braking and return to aconventional braking mode.

As noted earlier, in this enhanced mode, the valves such as 41 and 43are duty factor modulated to maintain braking pressure near the peak ofthe mu-slip curve. Of course, the reapply pressure should not exceed theoperator commanded pressure. Thus, controller 33 places an upper boundor limit on the duty cycle at 65 based on the commanded pressure 125 asindicated by pressure sensors such as 29 and 31. In either anti-skidmode 69 or 71, should a skid no longer be indicated or braking no longercalled for, the system returns to normal operator commanded braking at81.

The braking systems of FIGS. 1 or 5 require some additional logicillustrated generally by block 91 to keep the system under control.Comparing FIGS. 5 and 6, the wheel speed reference on line 39 should notbe allowed to lead all four wheel speeds in either direction. Thereference is tested against all four wheel speeds at 99 and the negativeoptstep is selected at 101 only if at least one new wheel speed is lessthan the reference. Similarly, the wheel speed reference is testedagainst all four wheel speeds at 97 and the positive optstep is selectedat 103 only if at least one wheel speed exceeds the reference. Block 105indicates the updating of both the acceleration and the change in thatacceleration. Similarly, block 107 indicates the updating of both thewheel speed reference and the change in that wheel speed reference. Thechange in slip velocity is determined at block 109 which corresponds toa change in the wheel speed reference. Block 111 indicates the updatingof both the individual measured wheel velocities and the changes inthose wheel velocities for each of four wheels. Actual individual wheelslip values are then computed at 117. If all four wheel slips areincreasing as indicated by a yes at 113, the slip sign is taken aspositive. Similarly, if all change in actual wheel speed slips aredecreasing as indicated by a yes at 115, the slip sign is taken asnegative. In equation (3) an optstep increment is added to increase thewheel speed reference when operation is in the undesirable region to theright of the maximum braking friction line 75, that is, when theacceleration/slip gradient is positive. Since only the signs of theacceleration and slip changes effect the sign of the quotient, actualdivision to obtain the gradient is unnecessary. Only the signs of thechanges need be considered. If both are the same as indicated by a yesat block 119 the sign of the quotient is positive and the wheel speedreference is incremented. If they differ, it is negative anddecrementation as indicated at 101 is called for. No optstep(incrementation by only the neutral step in Equation 3) is indicated at121 if no wheel speed has changed significantly from the wheel speedreference.

While a two-channel system has been described. The system can beimplemented in two, three or four-channel versions. A three-channelsystem seems best suited to front-wheel drive vehicles. Those skilled inthe art will devise many other adaptations, modifications and uses forthe present invention beyond those herein disclosed yet within the scopeof the present invention as set forth in the claims which follow.

What is claimed is:
 1. In the control of a vehicle anti-lock brakingsystem, the method of searching for an optimum wheel speed reference(39) comprising the steps of:determining (119) on which side of the peakof a mu-slip curve the vehicle is operating by repeatedly computing awheel speed reference to determining the sign of the ratio of the mostrecent change in measured acceleration to the most recent change incomputed wheel slip, and updating a previously computed wheel speedreference by incrementing (103) that previous reference by the sum of afirst amount and a second amount in the event the sign of the determinedratio is positive; incrementing (101) said previously computed wheelspeed reference by the difference between the first amount and thesecond amount in the event the sign of the determined ratio is negative;incrementing (88) said wheel speed reference by a value (79) whichchanges said wheel speed reference toward a peak (75) of the m-slipcurve thereby calculating an updated wheel speed reference, andutilizing (33) said updated wheel speed reference to controlappropriately the braking system.
 2. The method of claim 1 wherein thestep of determining comprises calculating the sign of the slope of themu-slip curve at the current vehicle operating point.
 3. The method ofclaim 2 wherein the value by which the wheel speed reference isincremented is the sum of a predetermined value (83) and positiveoptimizing value (85) when the slope is negative and is the differencebetween the predetermined value (83) and the positive optimizing value(85) when the slope is positive.